A method and device for calculating the chemical age of uranium minerals based on error transfer

Abstract

The present invention discloses a method and device for calculating the chemical age of uranium minerals based on error transfer, which are applied to the field of uranium geology science and technology. Aiming at the problems existing in the prior art that the calculated chemical age results of uranium minerals are not accurate enough and the precision is poor, the present invention determines the apparent age of each electron microprobe measurement point by importing the analysis result table of the chemical composition of uranium minerals by electron microprobe; according to the apparent age, using the error transfer formula, calculates the apparent age error of each electron microprobe measurement point; finally, through the weighted average algorithm, calculates the weighted average age. The present invention can accurately determine the error of the apparent age of uranium minerals during the process of calculating the chemical age of uranium minerals, has wide applicability, and the calculation method has clear logic. Since the influence of error transfer on the age result during the calculation process is fully considered, the calculation result is more accurate than the existing technology and can provide strong data support for determining a more accurate age of uranium minerals.

Description

Technical Field

[0001] The present invention belongs to the technical field of uranium geology science, and particularly relates to a uranium mineral age determination technology and device. Background Art

[0002] The uranium metallogenic age is an important content in the research of uranium deposits. Precise uranium chronology work plays a key role in clarifying multi-stage geological events, exploring and identifying more uranium deposits, and solving the current situation of uranium resource shortage.

[0003] In the past, for the determination of uranium mineral age, the isotope dilution method based on thermal ionization mass spectrometry was mostly used. This method simultaneously utilizes 238 U- 206 Pb, 235 U- 207 Pb two isotope decay series for age determination, and three independent ages can be obtained to internally correct the age. Although this method has high precision, due to the complexity of the origin of uranium minerals, it is often difficult to select pure samples, resulting in the obtained result being only a mixed age without reference value. Because the electron probe has the characteristics of in-situ, micro-area, and high resolution, it can avoid the altered and fractured parts of uranium minerals through backscattered images and obtain relatively reliable data points, so it is widely used in the age determination of uranium minerals. The main existing method for determining the chemical age of uranium minerals using an electron probe is as follows: calculating the apparent age of the measurement point using an empirical formula, and after artificially setting the size and type of the single-point error, calculating the weighted average of the apparent age through Isoplot / Ex software. This method has the problems that the chemical age result calculated by the empirical formula is not accurate enough and has poor precision. At the same time, in this calculation process, no clear method is given on how to calculate the specific single-year chemical age error, which further reduces the accuracy of the final calculation result. Therefore, there is an urgent need for a more optimized calculation method and device for the chemical age of uranium minerals based on error transfer. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a calculation method and device for the chemical age of uranium minerals based on error transfer, which can establish a more accurate chemical age of uranium minerals and provide a more scientific and reasonable basis for clarifying the uranium metallogenic age.

[0005] One of the technical solutions adopted by the present invention is: a calculation method for the chemical age of uranium minerals based on error transfer, including:

[0006] S1. Collect uranium mineral samples and conduct petrographic identification and electron probe analysis on the samples to obtain the electron probe chemical composition analysis result table of uranium minerals;

[0007] S2. Based on the uranium mineral electron probe chemical composition analysis result table obtained in step S1, use the iterative method to calculate the apparent age of each electron probe measurement point;

[0008] S3. Calculate the apparent age error of each electron probe measurement point according to the error propagation formula;

[0009] S4. According to the weighted average algorithm, use the apparent age and apparent age error of each electron probe measurement point to calculate the weighted average age.

[0010] The second technical solution adopted by the present invention is: a device for calculating the chemical age of uranium minerals based on error propagation, including:

[0011] A data collection module for obtaining the uranium mineral electron probe chemical composition analysis result table provided by the user;

[0012] An apparent age calculation module for calculating the apparent age of each electron probe measurement point according to the radioactive decay formula;

[0013] An apparent age error calculation module for calculating the apparent age error of each electron probe measurement point according to the error propagation formula and the chemical age errors of UO2, ThO2, and PbO;

[0014] A weighted average age calculation module for calculating the weighted average age according to the apparent age and error of each electron probe measurement point.

[0015] The beneficial effects of the present invention: A method and device for calculating the chemical age of uranium minerals based on error propagation proposed by the present invention determine the apparent age of each electron probe measurement point by importing the uranium mineral electron probe chemical composition analysis result table; according to the apparent age, use the error propagation formula to calculate the apparent age error of each electron probe measurement point; finally, calculate the weighted average age through the weighted average algorithm. The present invention can accurately determine the error of the apparent age of uranium minerals during the calculation of the chemical age of uranium minerals, has wide applicability, and the calculation method has clear logic. Since the influence of error propagation on the age result during the calculation process is fully considered, the calculation result is more accurate than the existing technology and can provide strong data support for determining a more accurate uranium mineral age. Description of the Drawings

[0016] Figure 1 It is a schematic diagram of the implementation process of the method for calculating the chemical age of uranium minerals based on error propagation in the embodiment of the present invention;

[0017] Figure 2 It is a schematic diagram of the structure of the device for calculating the chemical age of uranium minerals based on error propagation in the embodiment of the present invention;

[0018] Figure 3 This is the weighted age average graph in the embodiments of the present invention. Detailed implementation manners

[0019] To facilitate those skilled in the art to understand the technical content of the present invention, the content of the present invention will be further explained below with reference to the accompanying drawings.

[0020] A method and device for calculating the chemical age of uranium minerals based on error transfer, as Figure 1 shown, includes the following steps:

[0021] Step 1: Collect uranium mineral samples and conduct petrographic identification and electron probe analysis on the samples to obtain an electron probe chemical composition analysis result table;

[0022] Step 2: According to the obtained electron probe chemical composition analysis result table of uranium minerals, use the iterative method to calculate the apparent age of each electron probe measurement point;

[0023] Step 3: Calculate the apparent age error of each electron probe measurement point according to the error transfer formula;

[0024] Step 4: According to the weighted average algorithm, use the apparent age and error of each electron probe measurement point to calculate the weighted average age.

[0025] In the said Step 1, when collecting uranium mineral samples and conducting petrographic identification and electron probe analysis on the samples to obtain an electron probe chemical composition analysis result table, it is required that the samples are relatively fresh. After the samples are collected, the samples are made into electron probe slices, identified under the microscope, and uranium minerals with complete crystal forms and particle sizes greater than 50 μm are circled for electron probe chemical composition analysis.

[0026] In the said Step 2, according to the obtained electron probe chemical composition analysis result table of uranium minerals, using the iterative method to calculate the apparent age of each electron probe measurement point specifically includes:

[0027] When calculating the apparent age of natural uranium minerals using an electron probe, the following prerequisite conditions need to be met: (1) Since the formation of uranium minerals, the U-Th-Pb system has been in a closed state and has not undergone material exchange with the outside world; (2) The content of non-radiogenic lead in the system is extremely low and can be ignored; (3) The Pb component only comes from the radioactive decay of U and Th. When all the above three assumptions are valid, the isotopic composition of radioactive lead can be expressed as the following three equations:

[0028] 208 Pb = 232 Th{exp(λ 232 t)-1} (1)

[0029] 207 Pb = 235 U{exp(λ235 t) - 1} (2)

[0030] 206 Pb = 238 U{exp(λ 238 t) - 1} (3)

[0031] where the concentrations of U, Th, and Pb are in ppm; λ 232 , λ 235 , λ 238 are respectively 232 Th, 235 U, 238 the decay constants corresponding to U. Using the normal present-day uranium isotope ratio 235 U / 238 U = 1 / 137.88, then 235 U = (1 / 138.88)U = 0.0072U, 238 U = (137.88 / 138.88)U = 0.9928U, and the electron microprobe chemical dating method can be expressed as the following equation:

[0032] Pb = Th[exp(λ 232 t) - 1] + U[0.0072exp(λ 235 t) + 0.9928exp(λ 238 t) - 1] (4)

[0033] Since the contents of U, Th, and Pb measured by the electron microprobe are usually expressed in the form of oxides, Equation (4) can be rewritten as follows:

[0034] PbO / W Pb = (ThO2 / W Th )[exp(λ 232 t) - 1] + (UO2 / W U )[0.0072exp(λ 235 t) + 0.9928exp(λ 238 t) - 1] (5)

[0035] where UO2, ThO2, and PbO represent the percentage weights of the corresponding oxides; W Pb , W Th , W U represent the molecular weights of the corresponding oxides, and W Pb = 222(206 + 16), W Th = 264(232 + 32), W U= 270(238 + 32). Substitute the content values of UO2, ThO2, and PbO of the uranium mineral points measured by the electron microprobe into Equation (5). At the same time, the initial estimated age t = 100PbO%, and the initial age t is always higher than the actual true age. Using 0.1 Ma as the iteration amount, substitute it into Equation (5) and gradually decrease it until the calculated PbO content is consistent with the PbO content measured by the electron microprobe, then stop the iteration. Finally, a more accurate age can be obtained.

[0036] In the third step described above, calculate the apparent age error of each electron microprobe measurement point according to the error transfer formula, specifically including:

[0037] According to Equation (5), the following implicit function can be constructed to estimate the error of a single chemical age:

[0038] F(UO2, ThO2, PbO, t) = (ThO2 / W Th )[exp(λ 232 t) - 1] + (UO2 / W U )[0.0072exp(λ 235 t)

[0039] + 0.9928exp(λ 238 t) - 1] - PbO / W Pb (6)

[0040] By taking the partial derivatives of t, UO2, THO2, and PbO respectively, the following partial derivatives can be obtained:

[0041] F t = (ThO2 / 264)λ 232 exp(λ 232 t) + (UO2 / 270)[0.0072λ 235 exp(λ 235 t) + 0.9928λ 238 exp(λ 238 t)] (7a)

[0042] F UO2 = [0.0072exp(λ 235 t) + 0.9928exp(λ 238 t) - 1] / 270 (7b)

[0043] F ThO2 = [exp(λ 232 t) - 1] / 264 (7c)

[0044] F PbO = -1 / 222 (7d)

[0045] By combining equations (7a), (7b), (7c), and (7d), the apparent age error of the electron probe measurement point is obtained as follows:

[0046] Δt=|(F UO2 / Ft)|ΔUO2+|(FThO2 / Ft)|ΔThO2+|(F PbO / Ft)|ΔPbO (8)

[0047] Wherein, Δt, ΔUO2, ΔThO2 and ΔPbO represent the apparent age of the electron probe measurement point, the errors of UO2, ThO2, and PbO, respectively. ΔUO2, ΔThO2 and ΔPbO are generally between 2% and 5%. In practical applications, they can be set as needed. In this embodiment, ΔUO2, ΔThO2 and ΔPbO are all set to 5%; F UO2 / F t , F ThO2 / F t , and F PbO / F t represents the error transfer coefficient.

[0048] In step 4, the weighted average age is calculated according to the weighted average algorithm, where the apparent age of each electron probe measurement point is t i (i=1,2,3,……n), the apparent age error of each electron probe measurement point is σ i (i=1,2,3,...n), specifically including:

[0049] The weight is

[0050] The weighted average age is

[0051] The weighted mean error is

[0052] The weighted mean square deviation is

[0053] In order to explain the above-mentioned multi-stage uranium mineral chemical age calculation method more clearly, the present invention is further described in detail below by taking the granite pegmatite-type uranium deposit in Guangshigou area as an example.

[0054] Step 1: Collect uranium mineral samples in the Guangshigou area and conduct rock and mineral identification and electron probe analysis on the samples to obtain the electron probe chemical composition analysis result table. The samples must be relatively fresh. After the sample collection is completed, the samples are made into electron probe sheets and identified under a microscope. Uranium minerals with complete crystal shape, large particles and good preservation are circled for electron probe chemical composition analysis.

[0055] Step 2: According to the obtained electron microprobe chemical composition analysis result table of uranium minerals, use the iterative method to calculate the apparent age of each electron microprobe measurement point. It is required to substitute the contents of UO2, ThO2, and PbO at each measurement point into the following formula:

[0056] PbO / 222 = (ThO2 / 264)[exp(λ 232 t)-1] + (UO2 / 270)[0.0072exp(λ 235 t)+0.9928exp(λ 238 t)-1]

[0057] By the iterative method, set the initial estimated age t = 100PbO%, and the initial age t is always higher than the actual true age. Take 0.1 Ma as the iteration amount, substitute it into the above formula and gradually decrease until the calculated PbO content is consistent with the PbO content measured by the electron microprobe, then stop the iteration. Finally, a more accurate apparent age can be obtained. The range of the apparent ages of the 23 electron microprobe measurement points obtained this time is between 381.93 - 427.81 Ma, and the data is relatively concentrated. The calculation results are shown in Table 1.

[0058] Step 3: Calculate the error of the apparent age of each electron microprobe measurement point according to the error propagation formula. The following implicit function can be constructed to estimate the error of a single chemical age:

[0059] F(UO2, ThO2, PbO, t) = (ThO2 / W Th )[exp(λ 232 )[exp(λ U t)-1] + (UO2 / W 235 )[0.0072exp(λ 238 t)+0.9928exp(λ Pb

[0060] Respectively, by taking the partial derivatives of t, UO2, ThO2, and PbO, the following partial derivatives can be obtained:

[0061] F t = (ThO2 / 264)λ 232 exp(λ 232 t)+(UO2 / 270)[0.0072λ 235 exp(λ 235 t)+0.9928λ 238 exp(λ 238 t)]

[0062] F UO2 = [0.0072exp(λ 235 t)+0.9928exp(λ 238t)-1] / 270

[0063] F ThO2 =[exp(λ 232 t)-1] / 264

[0064] F PbO =-1 / 222

[0065] By combining equations (7a), (7b), (7c), and (7d), the apparent age error of the electron probe measurement point is obtained as follows:

[0066] Δt=|(F UO2 / Ft)|ΔUO2+|(FThO2 / Ft)|ΔThO2+|(F PbO / Ft)|ΔPbO

[0067] Where Δt, ΔUO2, ΔThO2 and ΔPbO represent the errors of apparent age, UO2, ThO2, and PbO, respectively; F UO2 / F t , FThO2 / F t , and F PbO / F t Represents the error transfer coefficient. The apparent age error of the electron probe measurement points analyzed this time is determined based on 5% of the UO2, ThO2, and PbO content (the error type is 2σ). By substituting the error (5%) of the UO2, ThO2, and PbO content into the above formula, the apparent age error of each electron probe measurement point can be calculated. The apparent age error range of the 23 crystalline uranium ore electron probe measurement points calculated this time is between 19.82-22.16Ma. The calculation results are shown in Table 1.

[0068] Table 1 Uranium mineral apparent age and error calculation results

[0069]

[0070]

[0071] Step 4: According to the weighted average algorithm, the weighted average age is calculated using the apparent age and error of each electron probe measurement point:

[0072] The weight is

[0073] The weighted average age is

[0074] The weighted mean error is

[0075] The weighted mean square deviation is

[0076] Based on the apparent ages and errors of each electron probe measurement point, the weighted average age (Mean) shown as Figure 3 follows is calculated to be 416.76 ± 4.53 Ma, with MSWD = 1.53; Figure 3 where MSWD is the full spelling of mean squared weighted deviation, representing the weighted mean square deviation; Age represents age, and the box heights are 2σ, that is Figure 3 the box heights in it are 2σ.

[0077] Based on the same inventive concept, the present invention also proposes a device for calculating the chemical age of uranium minerals based on error propagation. Refer to Figure 2 , since the principle of this device for solving problems is similar to that of the method for calculating the chemical age of uranium minerals based on error propagation, the implementation of this device can refer to the implementation of the method for calculating the chemical age of uranium minerals based on error propagation, and the repeated parts will not be elaborated here. A device for calculating the chemical age of uranium minerals based on error propagation according to the present invention includes:

[0078] A data collection module for obtaining the electron probe chemical composition analysis result table provided by the user;

[0079] An apparent age calculation module for calculating the apparent age and error of each electron probe measurement point according to the radioactive decay formula;

[0080] An apparent age error calculation module for calculating the apparent age error of each electron probe measurement point according to the error propagation formula and the errors of UO2, ThO2, and PbO;

[0081] A weighted average age calculation module for calculating the weighted average age according to the apparent ages and errors of each electron probe measurement point.

[0082] Those of ordinary skill in the art will realize that the embodiments described here are for helping readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, various changes and modifications can be made to the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of the claims of the present invention.

Claims

1. A method for calculating the chemical age of uranium minerals based on error transfer, characterized in that Including: S1. Collect uranium mineral samples, conduct petrographic identification and electron probe analysis on the samples, and obtain the electron probe chemical composition analysis result table of uranium minerals; S2. According to the electron probe chemical composition analysis result table of uranium minerals obtained in step S1, calculate the apparent age of each electron probe measurement point by using the iterative method; S3. Calculate the apparent age error of each electron probe measurement point according to the error propagation formula; Step S3 is specifically: S31. Estimate the error of a single chemical age by constructing an implicit function; Obtain the error expression of a single chemical age: F(UO2, ThO2, PbO, t) = (ThO2 / W Th )[exp(λ 232 t) - 1] + (UO2 / W U )[0.0072exp(λ 235 t) + 0.9928exp(λ 238 t) - 1] - PbO / W Pb ; t represents the estimated age, UO2, ThO2, and PbO represent the percentage weights of the corresponding oxides respectively, λ 232 , λ 235 , λ 238 are respectively 232 Th, 235 U, 238 U's decay constants; W Pb , W Th , W U represent the molecular weights of UO2, ThO2, and PbO respectively; S32. Respectively take the partial derivatives of the error expression for a single chemical age with respect to \(t\), \(UO_2\), \(ThO_2\), and \(PbO\) to obtain their respective corresponding partial derivatives \(F\) t 、\(F\) UO2 、\(F\) ThO2 、\(F\) PbO ; S33. Based on the error propagation formula, the apparent age error of the electron probe measurement point is obtained as: Δt = |(F UO2 / F t )|ΔUO2 + |(F ThO2 / F t )|ΔThO2 + |(F PbO / F t )|ΔPbO Where Δt represents the apparent age of the electron probe measurement point, ΔUO2 represents the error of UO2, ΔThO2 represents the error of ThO2, and ΔPbO represents the error of PbO; F UO2 / F t 、F ThO2 / F t 、F PbO / F t represent the error transfer coefficients; S4. According to the weighted average algorithm, calculate the weighted average age by using the apparent age and apparent age error of each electron probe measurement point.

2. The uranium mineral chemical age calculation method based on error transfer according to claim 1, characterized in that The electron probe chemical composition analysis result table of uranium minerals includes the contents of UO2, ThO2, and PbO at each electron probe measurement point.

3. A method for calculating the chemical age of uranium minerals based on error transfer according to claim 2, characterized in that, Step S2 is specifically: S21. According to the radioactive decay formulas of U, Th, and Pb respectively, the expression of the electron probe chemical dating method is obtained as: PbO / W Pb =(ThO2 / W Th )[exp(λ 232 )t - 1] + (UO2 / W U )[0.0072exp(λ 235 )t + 0.9928exp(λ 238 )t - 1] S22. Set the initial estimated age t = 100PbO%; S23. Substitute the contents of UO2, ThO2, and PbO at each electron probe measurement point in the electron probe chemical composition analysis result table of uranium minerals into the expression in step S21; if the calculated PbO content is consistent with the PbO content measured by the electron probe, execute step S25; otherwise, execute step S24; S24. Decrease t by 0.1 Ma and return to step S23; S25. Stop the iteration and use the t value corresponding to the current iteration as the apparent age of this electron probe measurement point.

4. A method for calculating the chemical age of uranium minerals based on error transfer according to claim 3, characterized in that, The weighted average age calculation formula described in step S4 is: where t i is the apparent age of the i-th electron probe measurement point, i = 1, 2, 3, …… n, where n is the total number of electron probe measurement points, and W i is the weight corresponding to the apparent age of the i-th electron probe measurement point.

5. A method for calculating the chemical age of uranium minerals based on error transfer according to claim 4, characterized in that W i Calculated based on the apparent age error of the electron probe measurement points.

6. A uranium mineral chemical age calculation device based on error transfer, characterized in that, Including: A data collection module, used to obtain the electron probe chemical composition analysis result table provided by the user; An apparent age calculation module, used to calculate the apparent age of each electron probe measurement point according to the radioactive decay formula and the electron probe chemical composition analysis result table of uranium minerals; An apparent age error calculation module, used to calculate the apparent age error of each electron probe measurement point according to the error propagation formula, the chemical age errors of UO2, ThO2, and PbO; The implementation process of the apparent age error calculation module is: The chemical age error expressions of UO2, ThO2, and PbO are: F(UO2, ThO2, PbO, t) = (ThO2 / W Th )[exp(λ 232 t) - 1] + (UO2 / W U )[0.0072exp(λ 235 t) + 0.9928exp(λ 238 t) - 1] - PbO / W Pb ; where t represents the estimated age, and UO2, ThO2, and PbO represent the percentage weights of the corresponding oxides respectively; The error expressions for the chemical ages of UO2, ThO2, and PbO are respectively differentiated with respect to t, UO2, ThO2, and PbO to obtain their respective partial derivatives F t , F UO2 , F ThO2 , F PbO ; Based on the error propagation formula, the apparent age error of the electron probe measurement point is obtained as: Δt = |(F UO2 / F t )|ΔUO2 + |(F ThO2 / F t )|ΔThO2 + |(F PbO / F t )|ΔPbO Wherein, Δt represents the apparent age of the electron probe measurement point, ΔUO2 represents the error of UO2, ΔThO2 represents the error of ThO2, and ΔPbO represents the error of PbO; F UO2 / F t 、F ThO2 / F t 、F PbO / F t represent the error transfer coefficients; A weighted average age calculation module, used to calculate the weighted average age according to the apparent age and apparent age error of each electron probe measurement point.

Images